   Chapter 9, Problem 12RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 7-20, find each limit, if it exists. 12.   lim x → − 1 2 x 2 − 1 4 6 x 2 + x − 1

To determine

To calculate: The value of the limit limx12x2146x2+x1.

Explanation

Given Information:

The provided limit is limx12x2146x2+x1.

Formula used:

A limit limxcx can be simplified as,

limxcx=c

According to the property of difference of squares,

a2b2=(a+b)(ab)

Calculation:

Consider the provided limit,

limx12x2146x2+x1

Simplify the limit by substituting 12 for x,

limx12x2146x2+x1=(12)2146(12)2+(12)1=14146(14)+122=03232=00

Since, the limit has 00 indeterminate form at x=12.

Thus, reduce the fraction, by factorizing the denominator and apply the property of difference of squares in numerator,

limx12x2(12)26x2+x1=limx12(x12)(x+12)6x2+3x2x1=limx12

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